Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.02728 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929760222838784 |
|---|---|
| author | Liu, Xu Culver, Adrian B. Harper, Fenner Roy, Rahul |
| author_facet | Liu, Xu Culver, Adrian B. Harper, Fenner Roy, Rahul |
| contents | Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02728 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of unitary operators by local generatability Liu, Xu Culver, Adrian B. Harper, Fenner Roy, Rahul Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics Periodically driven (Floquet) systems can exhibit possibilities beyond what can be obtained in equilibrium. Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify noninteracting unitaries in all dimensions on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence. |
| title | Classification of unitary operators by local generatability |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2308.02728 |